McDowell was drafted by the Chicago White Sox in the first round (fifth pick) of the 1987 amateur draft. After only six games in the minor leagues, he made his Major League debut on September 15, 1987. He pitched seven shutout innings against the Minnesota Twins that day to pick up the win. In four starts, he was 3-0 with a 1.93 ERA.

By the early 1990s, he had established himself as one of the most dependable pitchers in the game, pitching effectively and recording over 250 innings each season from 1991 to 1993, he was selected to the Major League Baseball All-Star Game each of those years. He won 20 games in 1992 and 22 in 1993, when he won the American LeagueCy Young Award and led the White Sox to the postseason (they lost in the 1993 American League Championship Series to the Toronto Blue Jays). From 1988 until 1995, his season ERA was consistently between 3.00 and 4.00, well below the league average. In 1993, he set a modern (post-1950) record by recording a decision in each of his first 27 starts.